LMFDB - Embedded newform 80.2.j.a.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(43,80)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("80.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	80.43
Dual form			80.2.j.a.67.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} -2.00000i q^{3} +2.00000i q^{4} +(1.00000 - 2.00000i) q^{5} +(2.00000 - 2.00000i) q^{6} +(-3.00000 + 3.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} -1.00000 q^{9} +(3.00000 - 1.00000i) q^{10} +(-1.00000 + 1.00000i) q^{11} +4.00000 q^{12} -2.00000 q^{13} -6.00000 q^{14} +(-4.00000 - 2.00000i) q^{15} -4.00000 q^{16} +(1.00000 - 1.00000i) q^{17} +(-1.00000 - 1.00000i) q^{18} +(3.00000 - 3.00000i) q^{19} +(4.00000 + 2.00000i) q^{20} +(6.00000 + 6.00000i) q^{21} -2.00000 q^{22} +(-1.00000 - 1.00000i) q^{23} +(4.00000 + 4.00000i) q^{24} +(-3.00000 - 4.00000i) q^{25} +(-2.00000 - 2.00000i) q^{26} -4.00000i q^{27} +(-6.00000 - 6.00000i) q^{28} +(7.00000 + 7.00000i) q^{29} +(-2.00000 - 6.00000i) q^{30} -2.00000i q^{31} +(-4.00000 - 4.00000i) q^{32} +(2.00000 + 2.00000i) q^{33} +2.00000 q^{34} +(3.00000 + 9.00000i) q^{35} -2.00000i q^{36} -6.00000 q^{37} +6.00000 q^{38} +4.00000i q^{39} +(2.00000 + 6.00000i) q^{40} +4.00000i q^{41} +12.0000i q^{42} +4.00000 q^{43} +(-2.00000 - 2.00000i) q^{44} +(-1.00000 + 2.00000i) q^{45} -2.00000i q^{46} +(7.00000 + 7.00000i) q^{47} +8.00000i q^{48} -11.0000i q^{49} +(1.00000 - 7.00000i) q^{50} +(-2.00000 - 2.00000i) q^{51} -4.00000i q^{52} -8.00000i q^{53} +(4.00000 - 4.00000i) q^{54} +(1.00000 + 3.00000i) q^{55} -12.0000i q^{56} +(-6.00000 - 6.00000i) q^{57} +14.0000i q^{58} +(-3.00000 - 3.00000i) q^{59} +(4.00000 - 8.00000i) q^{60} +(-1.00000 + 1.00000i) q^{61} +(2.00000 - 2.00000i) q^{62} +(3.00000 - 3.00000i) q^{63} -8.00000i q^{64} +(-2.00000 + 4.00000i) q^{65} +4.00000i q^{66} +4.00000 q^{67} +(2.00000 + 2.00000i) q^{68} +(-2.00000 + 2.00000i) q^{69} +(-6.00000 + 12.0000i) q^{70} +(2.00000 - 2.00000i) q^{72} +(-3.00000 + 3.00000i) q^{73} +(-6.00000 - 6.00000i) q^{74} +(-8.00000 + 6.00000i) q^{75} +(6.00000 + 6.00000i) q^{76} -6.00000i q^{77} +(-4.00000 + 4.00000i) q^{78} -8.00000 q^{79} +(-4.00000 + 8.00000i) q^{80} -11.0000 q^{81} +(-4.00000 + 4.00000i) q^{82} -2.00000i q^{83} +(-12.0000 + 12.0000i) q^{84} +(-1.00000 - 3.00000i) q^{85} +(4.00000 + 4.00000i) q^{86} +(14.0000 - 14.0000i) q^{87} -4.00000i q^{88} +6.00000 q^{89} +(-3.00000 + 1.00000i) q^{90} +(6.00000 - 6.00000i) q^{91} +(2.00000 - 2.00000i) q^{92} -4.00000 q^{93} +14.0000i q^{94} +(-3.00000 - 9.00000i) q^{95} +(-8.00000 + 8.00000i) q^{96} +(-11.0000 + 11.0000i) q^{97} +(11.0000 - 11.0000i) q^{98} +(1.00000 - 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{5} + 4 q^{6} - 6 q^{7} - 4 q^{8} - 2 q^{9} + 6 q^{10} - 2 q^{11} + 8 q^{12} - 4 q^{13} - 12 q^{14} - 8 q^{15} - 8 q^{16} + 2 q^{17} - 2 q^{18} + 6 q^{19} + 8 q^{20} + 12 q^{21} - 4 q^{22}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^5 + 4 * q^6 - 6 * q^7 - 4 * q^8 - 2 * q^9 + 6 * q^10 - 2 * q^11 + 8 * q^12 - 4 * q^13 - 12 * q^14 - 8 * q^15 - 8 * q^16 + 2 * q^17 - 2 * q^18 + 6 * q^19 + 8 * q^20 + 12 * q^21 - 4 * q^22 - 2 * q^23 + 8 * q^24 - 6 * q^25 - 4 * q^26 - 12 * q^28 + 14 * q^29 - 4 * q^30 - 8 * q^32 + 4 * q^33 + 4 * q^34 + 6 * q^35 - 12 * q^37 + 12 * q^38 + 4 * q^40 + 8 * q^43 - 4 * q^44 - 2 * q^45 + 14 * q^47 + 2 * q^50 - 4 * q^51 + 8 * q^54 + 2 * q^55 - 12 * q^57 - 6 * q^59 + 8 * q^60 - 2 * q^61 + 4 * q^62 + 6 * q^63 - 4 * q^65 + 8 * q^67 + 4 * q^68 - 4 * q^69 - 12 * q^70 + 4 * q^72 - 6 * q^73 - 12 * q^74 - 16 * q^75 + 12 * q^76 - 8 * q^78 - 16 * q^79 - 8 * q^80 - 22 * q^81 - 8 * q^82 - 24 * q^84 - 2 * q^85 + 8 * q^86 + 28 * q^87 + 12 * q^89 - 6 * q^90 + 12 * q^91 + 4 * q^92 - 8 * q^93 - 6 * q^95 - 16 * q^96 - 22 * q^97 + 22 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$		−	2.00000i		−	1.15470i	−0.816497	−	0.577350i	$-0.804087\pi$
$3$		−	2.00000i		−	1.15470i	0.816497	−	0.577350i	$-0.195913\pi$
$4$			2.00000i			1.00000i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$6$	2.00000	−	2.00000i	0.816497	−	0.816497i
$7$	−3.00000	+	3.00000i	−1.13389	+	1.13389i	−0.144370	+	0.989524i	$0.546115\pi$
$7$	−3.00000	+	3.00000i	−1.13389	+	1.13389i	−0.989524	+	0.144370i	$0.953885\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	−1.00000			−0.333333
$10$	3.00000	−	1.00000i	0.948683	−	0.316228i
$11$	−1.00000	+	1.00000i	−0.301511	+	0.301511i	−0.841605	−	0.540094i	$-0.818389\pi$
$11$	−1.00000	+	1.00000i	−0.301511	+	0.301511i	0.540094	+	0.841605i	$0.318389\pi$
$12$	4.00000			1.15470
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$	−6.00000			−1.60357
$15$	−4.00000	−	2.00000i	−1.03280	−	0.516398i
$16$	−4.00000			−1.00000
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	−0.575363	−	0.817898i	$-0.695139\pi$
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	0.817898	+	0.575363i	$0.195139\pi$
$18$	−1.00000	−	1.00000i	−0.235702	−	0.235702i
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	−0.273597	−	0.961844i	$-0.588214\pi$
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	0.961844	+	0.273597i	$0.0882135\pi$
$20$	4.00000	+	2.00000i	0.894427	+	0.447214i
$21$	6.00000	+	6.00000i	1.30931	+	1.30931i
$22$	−2.00000			−0.426401
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	0.595121	−	0.803636i	$-0.297104\pi$
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	−0.803636	+	0.595121i	$0.797104\pi$
$24$	4.00000	+	4.00000i	0.816497	+	0.816497i
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$	−2.00000	−	2.00000i	−0.392232	−	0.392232i
$27$		−	4.00000i		−	0.769800i
$28$	−6.00000	−	6.00000i	−1.13389	−	1.13389i
$29$	7.00000	+	7.00000i	1.29987	+	1.29987i	0.928477	+	0.371391i	$0.121119\pi$
$29$	7.00000	+	7.00000i	1.29987	+	1.29987i	0.371391	+	0.928477i	$0.378881\pi$
$30$	−2.00000	−	6.00000i	−0.365148	−	1.09545i
$31$		−	2.00000i		−	0.359211i	−0.983739	−	0.179605i	$-0.942518\pi$
$31$		−	2.00000i		−	0.359211i	0.983739	−	0.179605i	$-0.0574821\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	2.00000	+	2.00000i	0.348155	+	0.348155i
$34$	2.00000			0.342997
$35$	3.00000	+	9.00000i	0.507093	+	1.52128i
$36$		−	2.00000i		−	0.333333i
$37$	−6.00000			−0.986394			−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000			−0.986394			−0.493197	+	0.869918i	$0.664172\pi$
$38$	6.00000			0.973329
$39$			4.00000i			0.640513i
$40$	2.00000	+	6.00000i	0.316228	+	0.948683i
$41$			4.00000i			0.624695i	0.949968	+	0.312348i	$0.101115\pi$
$41$			4.00000i			0.624695i	−0.949968	+	0.312348i	$0.898885\pi$
$42$			12.0000i			1.85164i
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	−2.00000	−	2.00000i	−0.301511	−	0.301511i
$45$	−1.00000	+	2.00000i	−0.149071	+	0.298142i
$46$		−	2.00000i		−	0.294884i
$47$	7.00000	+	7.00000i	1.02105	+	1.02105i	0.999774	+	0.0212814i	$0.00677460\pi$
$47$	7.00000	+	7.00000i	1.02105	+	1.02105i	0.0212814	+	0.999774i	$0.493225\pi$
$48$			8.00000i			1.15470i
$49$		−	11.0000i		−	1.57143i
$50$	1.00000	−	7.00000i	0.141421	−	0.989949i
$51$	−2.00000	−	2.00000i	−0.280056	−	0.280056i
$52$		−	4.00000i		−	0.554700i
$53$		−	8.00000i		−	1.09888i	−0.835532	−	0.549442i	$-0.814840\pi$
$53$		−	8.00000i		−	1.09888i	0.835532	−	0.549442i	$-0.185160\pi$
$54$	4.00000	−	4.00000i	0.544331	−	0.544331i
$55$	1.00000	+	3.00000i	0.134840	+	0.404520i
$56$		−	12.0000i		−	1.60357i
$57$	−6.00000	−	6.00000i	−0.794719	−	0.794719i
$58$			14.0000i			1.83829i
$59$	−3.00000	−	3.00000i	−0.390567	−	0.390567i	0.484323	−	0.874889i	$-0.339066\pi$
$59$	−3.00000	−	3.00000i	−0.390567	−	0.390567i	−0.874889	+	0.484323i	$0.839066\pi$
$60$	4.00000	−	8.00000i	0.516398	−	1.03280i
$61$	−1.00000	+	1.00000i	−0.128037	+	0.128037i	−0.768221	−	0.640184i	$-0.778858\pi$
$61$	−1.00000	+	1.00000i	−0.128037	+	0.128037i	0.640184	+	0.768221i	$0.278858\pi$
$62$	2.00000	−	2.00000i	0.254000	−	0.254000i
$63$	3.00000	−	3.00000i	0.377964	−	0.377964i
$64$		−	8.00000i		−	1.00000i
$65$	−2.00000	+	4.00000i	−0.248069	+	0.496139i
$66$			4.00000i			0.492366i
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	2.00000	+	2.00000i	0.242536	+	0.242536i
$69$	−2.00000	+	2.00000i	−0.240772	+	0.240772i
$70$	−6.00000	+	12.0000i	−0.717137	+	1.43427i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	2.00000	−	2.00000i	0.235702	−	0.235702i
$73$	−3.00000	+	3.00000i	−0.351123	+	0.351123i	−0.860527	−	0.509404i	$-0.829866\pi$
$73$	−3.00000	+	3.00000i	−0.351123	+	0.351123i	0.509404	+	0.860527i	$0.329866\pi$
$74$	−6.00000	−	6.00000i	−0.697486	−	0.697486i
$75$	−8.00000	+	6.00000i	−0.923760	+	0.692820i
$76$	6.00000	+	6.00000i	0.688247	+	0.688247i
$77$		−	6.00000i		−	0.683763i
$78$	−4.00000	+	4.00000i	−0.452911	+	0.452911i
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$	−4.00000	+	8.00000i	−0.447214	+	0.894427i
$81$	−11.0000			−1.22222
$82$	−4.00000	+	4.00000i	−0.441726	+	0.441726i
$83$		−	2.00000i		−	0.219529i	−0.993958	−	0.109764i	$-0.964990\pi$
$83$		−	2.00000i		−	0.219529i	0.993958	−	0.109764i	$-0.0350096\pi$
$84$	−12.0000	+	12.0000i	−1.30931	+	1.30931i
$85$	−1.00000	−	3.00000i	−0.108465	−	0.325396i
$86$	4.00000	+	4.00000i	0.431331	+	0.431331i
$87$	14.0000	−	14.0000i	1.50096	−	1.50096i
$88$		−	4.00000i		−	0.426401i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	−3.00000	+	1.00000i	−0.316228	+	0.105409i
$91$	6.00000	−	6.00000i	0.628971	−	0.628971i
$92$	2.00000	−	2.00000i	0.208514	−	0.208514i
$93$	−4.00000			−0.414781
$94$			14.0000i			1.44399i
$95$	−3.00000	−	9.00000i	−0.307794	−	0.923381i
$96$	−8.00000	+	8.00000i	−0.816497	+	0.816497i
$97$	−11.0000	+	11.0000i	−1.11688	+	1.11688i	−0.124684	+	0.992196i	$0.539792\pi$
$97$	−11.0000	+	11.0000i	−1.11688	+	1.11688i	−0.992196	+	0.124684i	$0.960208\pi$
$98$	11.0000	−	11.0000i	1.11117	−	1.11117i
$99$	1.00000	−	1.00000i	0.100504	−	0.100504i
$100$	8.00000	−	6.00000i	0.800000	−	0.600000i
$101$	−5.00000	−	5.00000i	−0.497519	−	0.497519i	0.413146	−	0.910665i	$-0.364430\pi$
$101$	−5.00000	−	5.00000i	−0.497519	−	0.497519i	−0.910665	+	0.413146i	$0.864430\pi$
$102$		−	4.00000i		−	0.396059i
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	0.416480	−	0.909145i	$-0.363264\pi$
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	−0.909145	+	0.416480i	$0.863264\pi$
$104$	4.00000	−	4.00000i	0.392232	−	0.392232i
$105$	18.0000	−	6.00000i	1.75662	−	0.585540i
$106$	8.00000	−	8.00000i	0.777029	−	0.777029i
$107$			6.00000i			0.580042i	0.957020	+	0.290021i	$0.0936623\pi$
$107$			6.00000i			0.580042i	−0.957020	+	0.290021i	$0.906338\pi$
$108$	8.00000			0.769800
$109$	−5.00000	−	5.00000i	−0.478913	−	0.478913i	0.425871	−	0.904784i	$-0.359968\pi$
$109$	−5.00000	−	5.00000i	−0.478913	−	0.478913i	−0.904784	+	0.425871i	$0.859968\pi$
$110$	−2.00000	+	4.00000i	−0.190693	+	0.381385i
$111$			12.0000i			1.13899i
$112$	12.0000	−	12.0000i	1.13389	−	1.13389i
$113$	13.0000	+	13.0000i	1.22294	+	1.22294i	0.966583	+	0.256354i	$0.0825214\pi$
$113$	13.0000	+	13.0000i	1.22294	+	1.22294i	0.256354	+	0.966583i	$0.417479\pi$
$114$		−	12.0000i		−	1.12390i
$115$	−3.00000	+	1.00000i	−0.279751	+	0.0932505i
$116$	−14.0000	+	14.0000i	−1.29987	+	1.29987i
$117$	2.00000			0.184900
$118$		−	6.00000i		−	0.552345i
$119$			6.00000i			0.550019i
$120$	12.0000	−	4.00000i	1.09545	−	0.365148i
$121$			9.00000i			0.818182i
$122$	−2.00000			−0.181071
$123$	8.00000			0.721336
$124$	4.00000			0.359211
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$	6.00000			0.534522
$127$	7.00000	+	7.00000i	0.621150	+	0.621150i	0.945825	−	0.324676i	$-0.105255\pi$
$127$	7.00000	+	7.00000i	0.621150	+	0.621150i	−0.324676	+	0.945825i	$0.605255\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$		−	8.00000i		−	0.704361i
$130$	−6.00000	+	2.00000i	−0.526235	+	0.175412i
$131$	−7.00000	−	7.00000i	−0.611593	−	0.611593i	0.331768	−	0.943361i	$-0.392355\pi$
$131$	−7.00000	−	7.00000i	−0.611593	−	0.611593i	−0.943361	+	0.331768i	$0.892355\pi$
$132$	−4.00000	+	4.00000i	−0.348155	+	0.348155i
$133$			18.0000i			1.56080i
$134$	4.00000	+	4.00000i	0.345547	+	0.345547i
$135$	−8.00000	−	4.00000i	−0.688530	−	0.344265i
$136$			4.00000i			0.342997i
$137$	9.00000	+	9.00000i	0.768922	+	0.768922i	0.977917	−	0.208995i	$-0.0670192\pi$
$137$	9.00000	+	9.00000i	0.768922	+	0.768922i	−0.208995	+	0.977917i	$0.567019\pi$
$138$	−4.00000			−0.340503
$139$	9.00000	+	9.00000i	0.763370	+	0.763370i	0.976930	−	0.213560i	$-0.0685059\pi$
$139$	9.00000	+	9.00000i	0.763370	+	0.763370i	−0.213560	+	0.976930i	$0.568506\pi$
$140$	−18.0000	+	6.00000i	−1.52128	+	0.507093i
$141$	14.0000	−	14.0000i	1.17901	−	1.17901i
$142$		0			0
$143$	2.00000	−	2.00000i	0.167248	−	0.167248i
$144$	4.00000			0.333333
$145$	21.0000	−	7.00000i	1.74396	−	0.581318i
$146$	−6.00000			−0.496564
$147$	−22.0000			−1.81453
$148$		−	12.0000i		−	0.986394i
$149$	−1.00000	+	1.00000i	−0.0819232	+	0.0819232i	−0.746881	−	0.664958i	$-0.768450\pi$
$149$	−1.00000	+	1.00000i	−0.0819232	+	0.0819232i	0.664958	+	0.746881i	$0.268450\pi$
$150$	−14.0000	−	2.00000i	−1.14310	−	0.163299i
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$			12.0000i			0.973329i
$153$	−1.00000	+	1.00000i	−0.0808452	+	0.0808452i
$154$	6.00000	−	6.00000i	0.483494	−	0.483494i
$155$	−4.00000	−	2.00000i	−0.321288	−	0.160644i
$156$	−8.00000			−0.640513
$157$		−	20.0000i		−	1.59617i	−0.602542	−	0.798087i	$-0.705846\pi$
$157$		−	20.0000i		−	1.59617i	0.602542	−	0.798087i	$-0.294154\pi$
$158$	−8.00000	−	8.00000i	−0.636446	−	0.636446i
$159$	−16.0000			−1.26888
$160$	−12.0000	+	4.00000i	−0.948683	+	0.316228i
$161$	6.00000			0.472866
$162$	−11.0000	−	11.0000i	−0.864242	−	0.864242i
$163$			14.0000i			1.09656i	0.836293	+	0.548282i	$0.184718\pi$
$163$			14.0000i			1.09656i	−0.836293	+	0.548282i	$0.815282\pi$
$164$	−8.00000			−0.624695
$165$	6.00000	−	2.00000i	0.467099	−	0.155700i
$166$	2.00000	−	2.00000i	0.155230	−	0.155230i
$167$	−3.00000	+	3.00000i	−0.232147	+	0.232147i	−0.813588	−	0.581441i	$-0.802489\pi$
$167$	−3.00000	+	3.00000i	−0.232147	+	0.232147i	0.581441	+	0.813588i	$0.302489\pi$
$168$	−24.0000			−1.85164
$169$	−9.00000			−0.692308
$170$	2.00000	−	4.00000i	0.153393	−	0.306786i
$171$	−3.00000	+	3.00000i	−0.229416	+	0.229416i
$172$			8.00000i			0.609994i
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$	28.0000			2.12267
$175$	21.0000	+	3.00000i	1.58745	+	0.226779i
$176$	4.00000	−	4.00000i	0.301511	−	0.301511i
$177$	−6.00000	+	6.00000i	−0.450988	+	0.450988i
$178$	6.00000	+	6.00000i	0.449719	+	0.449719i
$179$	−5.00000	+	5.00000i	−0.373718	+	0.373718i	−0.868829	−	0.495112i	$-0.835127\pi$
$179$	−5.00000	+	5.00000i	−0.373718	+	0.373718i	0.495112	+	0.868829i	$0.335127\pi$
$180$	−4.00000	−	2.00000i	−0.298142	−	0.149071i
$181$	3.00000	+	3.00000i	0.222988	+	0.222988i	0.809756	−	0.586767i	$-0.199600\pi$
$181$	3.00000	+	3.00000i	0.222988	+	0.222988i	−0.586767	+	0.809756i	$0.699600\pi$
$182$	12.0000			0.889499
$183$	2.00000	+	2.00000i	0.147844	+	0.147844i
$184$	4.00000			0.294884
$185$	−6.00000	+	12.0000i	−0.441129	+	0.882258i
$186$	−4.00000	−	4.00000i	−0.293294	−	0.293294i
$187$			2.00000i			0.146254i
$188$	−14.0000	+	14.0000i	−1.02105	+	1.02105i
$189$	12.0000	+	12.0000i	0.872872	+	0.872872i
$190$	6.00000	−	12.0000i	0.435286	−	0.870572i
$191$		−	18.0000i		−	1.30243i	−0.758891	−	0.651217i	$-0.774259\pi$
$191$		−	18.0000i		−	1.30243i	0.758891	−	0.651217i	$-0.225741\pi$
$192$	−16.0000			−1.15470
$193$	−15.0000	−	15.0000i	−1.07972	−	1.07972i	−0.996534	−	0.0831899i	$-0.973489\pi$
$193$	−15.0000	−	15.0000i	−1.07972	−	1.07972i	−0.0831899	−	0.996534i	$-0.526511\pi$
$194$	−22.0000			−1.57951
$195$	8.00000	+	4.00000i	0.572892	+	0.286446i
$196$	22.0000			1.57143
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$	2.00000			0.142134
$199$		−	10.0000i		−	0.708881i	−0.935079	−	0.354441i	$-0.884671\pi$
$199$		−	10.0000i		−	0.708881i	0.935079	−	0.354441i	$-0.115329\pi$
$200$	14.0000	+	2.00000i	0.989949	+	0.141421i
$201$		−	8.00000i		−	0.564276i
$202$		−	10.0000i		−	0.703598i
$203$	−42.0000			−2.94782
$204$	4.00000	−	4.00000i	0.280056	−	0.280056i
$205$	8.00000	+	4.00000i	0.558744	+	0.279372i
$206$		−	10.0000i		−	0.696733i
$207$	1.00000	+	1.00000i	0.0695048	+	0.0695048i
$208$	8.00000			0.554700
$209$			6.00000i			0.415029i
$210$	24.0000	+	12.0000i	1.65616	+	0.828079i
$211$	−19.0000	−	19.0000i	−1.30801	−	1.30801i	−0.922847	−	0.385167i	$-0.874144\pi$
$211$	−19.0000	−	19.0000i	−1.30801	−	1.30801i	−0.385167	−	0.922847i	$-0.625856\pi$
$212$	16.0000			1.09888
$213$		0			0
$214$	−6.00000	+	6.00000i	−0.410152	+	0.410152i
$215$	4.00000	−	8.00000i	0.272798	−	0.545595i
$216$	8.00000	+	8.00000i	0.544331	+	0.544331i
$217$	6.00000	+	6.00000i	0.407307	+	0.407307i
$218$		−	10.0000i		−	0.677285i
$219$	6.00000	+	6.00000i	0.405442	+	0.405442i
$220$	−6.00000	+	2.00000i	−0.404520	+	0.134840i
$221$	−2.00000	+	2.00000i	−0.134535	+	0.134535i
$222$	−12.0000	+	12.0000i	−0.805387	+	0.805387i
$223$	9.00000	−	9.00000i	0.602685	−	0.602685i	−0.338340	−	0.941024i	$-0.609865\pi$
$223$	9.00000	−	9.00000i	0.602685	−	0.602685i	0.941024	+	0.338340i	$0.109865\pi$
$224$	24.0000			1.60357
$225$	3.00000	+	4.00000i	0.200000	+	0.266667i
$226$			26.0000i			1.72949i
$227$	12.0000			0.796468			0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000			0.796468			0.398234	+	0.917284i	$0.369623\pi$
$228$	12.0000	−	12.0000i	0.794719	−	0.794719i
$229$	−1.00000	+	1.00000i	−0.0660819	+	0.0660819i	−0.739375	−	0.673293i	$-0.764879\pi$
$229$	−1.00000	+	1.00000i	−0.0660819	+	0.0660819i	0.673293	+	0.739375i	$0.264879\pi$
$230$	−4.00000	−	2.00000i	−0.263752	−	0.131876i
$231$	−12.0000			−0.789542
$232$	−28.0000			−1.83829
$233$	9.00000	−	9.00000i	0.589610	−	0.589610i	−0.347916	−	0.937526i	$-0.613111\pi$
$233$	9.00000	−	9.00000i	0.589610	−	0.589610i	0.937526	+	0.347916i	$0.113111\pi$
$234$	2.00000	+	2.00000i	0.130744	+	0.130744i
$235$	21.0000	−	7.00000i	1.36989	−	0.456630i
$236$	6.00000	−	6.00000i	0.390567	−	0.390567i
$237$			16.0000i			1.03931i
$238$	−6.00000	+	6.00000i	−0.388922	+	0.388922i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	16.0000	+	8.00000i	1.03280	+	0.516398i
$241$	−14.0000			−0.901819			−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000			−0.901819			−0.450910	+	0.892570i	$0.648900\pi$
$242$	−9.00000	+	9.00000i	−0.578542	+	0.578542i
$243$			10.0000i			0.641500i
$244$	−2.00000	−	2.00000i	−0.128037	−	0.128037i
$245$	−22.0000	−	11.0000i	−1.40553	−	0.702764i
$246$	8.00000	+	8.00000i	0.510061	+	0.510061i
$247$	−6.00000	+	6.00000i	−0.381771	+	0.381771i
$248$	4.00000	+	4.00000i	0.254000	+	0.254000i
$249$	−4.00000			−0.253490
$250$	−13.0000	−	9.00000i	−0.822192	−	0.569210i
$251$	11.0000	−	11.0000i	0.694314	−	0.694314i	−0.268864	−	0.963178i	$-0.586648\pi$
$251$	11.0000	−	11.0000i	0.694314	−	0.694314i	0.963178	+	0.268864i	$0.0866483\pi$
$252$	6.00000	+	6.00000i	0.377964	+	0.377964i
$253$	2.00000			0.125739
$254$			14.0000i			0.878438i
$255$	−6.00000	+	2.00000i	−0.375735	+	0.125245i
$256$	16.0000			1.00000
$257$	13.0000	−	13.0000i	0.810918	−	0.810918i	−0.173854	−	0.984771i	$-0.555622\pi$
$257$	13.0000	−	13.0000i	0.810918	−	0.810918i	0.984771	+	0.173854i	$0.0556220\pi$
$258$	8.00000	−	8.00000i	0.498058	−	0.498058i
$259$	18.0000	−	18.0000i	1.11847	−	1.11847i
$260$	−8.00000	−	4.00000i	−0.496139	−	0.248069i
$261$	−7.00000	−	7.00000i	−0.433289	−	0.433289i
$262$		−	14.0000i		−	0.864923i
$263$	7.00000	+	7.00000i	0.431638	+	0.431638i	0.889185	−	0.457547i	$-0.151272\pi$
$263$	7.00000	+	7.00000i	0.431638	+	0.431638i	−0.457547	+	0.889185i	$0.651272\pi$
$264$	−8.00000			−0.492366
$265$	−16.0000	−	8.00000i	−0.982872	−	0.491436i
$266$	−18.0000	+	18.0000i	−1.10365	+	1.10365i
$267$		−	12.0000i		−	0.734388i
$268$			8.00000i			0.488678i
$269$	−1.00000	−	1.00000i	−0.0609711	−	0.0609711i	0.675964	−	0.736935i	$-0.263728\pi$
$269$	−1.00000	−	1.00000i	−0.0609711	−	0.0609711i	−0.736935	+	0.675964i	$0.763728\pi$
$270$	−4.00000	−	12.0000i	−0.243432	−	0.730297i
$271$			30.0000i			1.82237i	0.411997	+	0.911185i	$0.364831\pi$
$271$			30.0000i			1.82237i	−0.411997	+	0.911185i	$0.635169\pi$
$272$	−4.00000	+	4.00000i	−0.242536	+	0.242536i
$273$	−12.0000	−	12.0000i	−0.726273	−	0.726273i
$274$			18.0000i			1.08742i
$275$	7.00000	+	1.00000i	0.422116	+	0.0603023i
$276$	−4.00000	−	4.00000i	−0.240772	−	0.240772i
$277$	18.0000			1.08152			0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000			1.08152			0.540758	+	0.841178i	$0.318138\pi$
$278$			18.0000i			1.07957i
$279$			2.00000i			0.119737i
$280$	−24.0000	−	12.0000i	−1.43427	−	0.717137i
$281$		−	16.0000i		−	0.954480i	−0.878773	−	0.477240i	$-0.841637\pi$
$281$		−	16.0000i		−	0.954480i	0.878773	−	0.477240i	$-0.158363\pi$
$282$	28.0000			1.66738
$283$	12.0000			0.713326			0.356663	−	0.934233i	$-0.383914\pi$
$283$	12.0000			0.713326			0.356663	+	0.934233i	$0.383914\pi$
$284$		0			0
$285$	−18.0000	+	6.00000i	−1.06623	+	0.355409i
$286$	4.00000			0.236525
$287$	−12.0000	−	12.0000i	−0.708338	−	0.708338i
$288$	4.00000	+	4.00000i	0.235702	+	0.235702i
$289$			15.0000i			0.882353i
$290$	28.0000	+	14.0000i	1.64422	+	0.822108i
$291$	22.0000	+	22.0000i	1.28966	+	1.28966i
$292$	−6.00000	−	6.00000i	−0.351123	−	0.351123i
$293$		−	12.0000i		−	0.701047i	−0.936554	−	0.350524i	$-0.886004\pi$
$293$		−	12.0000i		−	0.701047i	0.936554	−	0.350524i	$-0.113996\pi$
$294$	−22.0000	−	22.0000i	−1.28307	−	1.28307i
$295$	−9.00000	+	3.00000i	−0.524000	+	0.174667i
$296$	12.0000	−	12.0000i	0.697486	−	0.697486i
$297$	4.00000	+	4.00000i	0.232104	+	0.232104i
$298$	−2.00000			−0.115857
$299$	2.00000	+	2.00000i	0.115663	+	0.115663i
$300$	−12.0000	−	16.0000i	−0.692820	−	0.923760i
$301$	−12.0000	+	12.0000i	−0.691669	+	0.691669i
$302$	8.00000	+	8.00000i	0.460348	+	0.460348i
$303$	−10.0000	+	10.0000i	−0.574485	+	0.574485i
$304$	−12.0000	+	12.0000i	−0.688247	+	0.688247i
$305$	1.00000	+	3.00000i	0.0572598	+	0.171780i
$306$	−2.00000			−0.114332
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$	12.0000			0.683763
$309$	−10.0000	+	10.0000i	−0.568880	+	0.568880i
$310$	−2.00000	−	6.00000i	−0.113592	−	0.340777i
$311$	16.0000			0.907277			0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000			0.907277			0.453638	+	0.891186i	$0.350126\pi$
$312$	−8.00000	−	8.00000i	−0.452911	−	0.452911i
$313$	13.0000	−	13.0000i	0.734803	−	0.734803i	−0.236764	−	0.971567i	$-0.576087\pi$
$313$	13.0000	−	13.0000i	0.734803	−	0.734803i	0.971567	+	0.236764i	$0.0760868\pi$
$314$	20.0000	−	20.0000i	1.12867	−	1.12867i
$315$	−3.00000	−	9.00000i	−0.169031	−	0.507093i
$316$		−	16.0000i		−	0.900070i
$317$		−	8.00000i		−	0.449325i	−0.974437	−	0.224662i	$-0.927872\pi$
$317$		−	8.00000i		−	0.449325i	0.974437	−	0.224662i	$-0.0721279\pi$
$318$	−16.0000	−	16.0000i	−0.897235	−	0.897235i
$319$	−14.0000			−0.783850
$320$	−16.0000	−	8.00000i	−0.894427	−	0.447214i
$321$	12.0000			0.669775
$322$	6.00000	+	6.00000i	0.334367	+	0.334367i
$323$		−	6.00000i		−	0.333849i
$324$		−	22.0000i		−	1.22222i
$325$	6.00000	+	8.00000i	0.332820	+	0.443760i
$326$	−14.0000	+	14.0000i	−0.775388	+	0.775388i
$327$	−10.0000	+	10.0000i	−0.553001	+	0.553001i
$328$	−8.00000	−	8.00000i	−0.441726	−	0.441726i
$329$	−42.0000			−2.31553
$330$	8.00000	+	4.00000i	0.440386	+	0.220193i
$331$	−21.0000	+	21.0000i	−1.15426	+	1.15426i	−0.168576	+	0.985689i	$0.553917\pi$
$331$	−21.0000	+	21.0000i	−1.15426	+	1.15426i	−0.985689	+	0.168576i	$0.946083\pi$
$332$	4.00000			0.219529
$333$	6.00000			0.328798
$334$	−6.00000			−0.328305
$335$	4.00000	−	8.00000i	0.218543	−	0.437087i
$336$	−24.0000	−	24.0000i	−1.30931	−	1.30931i
$337$	−11.0000	+	11.0000i	−0.599208	+	0.599208i	−0.940102	−	0.340894i	$-0.889270\pi$
$337$	−11.0000	+	11.0000i	−0.599208	+	0.599208i	0.340894	+	0.940102i	$0.389270\pi$
$338$	−9.00000	−	9.00000i	−0.489535	−	0.489535i
$339$	26.0000	−	26.0000i	1.41213	−	1.41213i
$340$	6.00000	−	2.00000i	0.325396	−	0.108465i
$341$	2.00000	+	2.00000i	0.108306	+	0.108306i
$342$	−6.00000			−0.324443
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	−8.00000	+	8.00000i	−0.431331	+	0.431331i
$345$	2.00000	+	6.00000i	0.107676	+	0.323029i
$346$	−6.00000	−	6.00000i	−0.322562	−	0.322562i
$347$		−	2.00000i		−	0.107366i	−0.998558	−	0.0536828i	$-0.982904\pi$
$347$		−	2.00000i		−	0.107366i	0.998558	−	0.0536828i	$-0.0170960\pi$
$348$	28.0000	+	28.0000i	1.50096	+	1.50096i
$349$	3.00000	+	3.00000i	0.160586	+	0.160586i	0.782826	−	0.622240i	$-0.213777\pi$
$349$	3.00000	+	3.00000i	0.160586	+	0.160586i	−0.622240	+	0.782826i	$0.713777\pi$
$350$	18.0000	+	24.0000i	0.962140	+	1.28285i
$351$			8.00000i			0.427008i
$352$	8.00000			0.426401
$353$	13.0000	+	13.0000i	0.691920	+	0.691920i	0.962654	−	0.270734i	$-0.0872664\pi$
$353$	13.0000	+	13.0000i	0.691920	+	0.691920i	−0.270734	+	0.962654i	$0.587266\pi$
$354$	−12.0000			−0.637793
$355$		0			0
$356$			12.0000i			0.635999i
$357$	12.0000			0.635107
$358$	−10.0000			−0.528516
$359$			14.0000i			0.738892i	0.929252	+	0.369446i	$0.120452\pi$
$359$			14.0000i			0.738892i	−0.929252	+	0.369446i	$0.879548\pi$
$360$	−2.00000	−	6.00000i	−0.105409	−	0.316228i
$361$			1.00000i			0.0526316i
$362$			6.00000i			0.315353i
$363$	18.0000			0.944755
$364$	12.0000	+	12.0000i	0.628971	+	0.628971i
$365$	3.00000	+	9.00000i	0.157027	+	0.471082i
$366$			4.00000i			0.209083i
$367$	−21.0000	−	21.0000i	−1.09619	−	1.09619i	−0.994852	−	0.101339i	$-0.967687\pi$
$367$	−21.0000	−	21.0000i	−1.09619	−	1.09619i	−0.101339	−	0.994852i	$-0.532313\pi$
$368$	4.00000	+	4.00000i	0.208514	+	0.208514i
$369$		−	4.00000i		−	0.208232i
$370$	−18.0000	+	6.00000i	−0.935775	+	0.311925i
$371$	24.0000	+	24.0000i	1.24602	+	1.24602i
$372$		−	8.00000i		−	0.414781i
$373$		−	4.00000i		−	0.207112i	−0.994624	−	0.103556i	$-0.966978\pi$
$373$		−	4.00000i		−	0.207112i	0.994624	−	0.103556i	$-0.0330221\pi$
$374$	−2.00000	+	2.00000i	−0.103418	+	0.103418i
$375$	4.00000	+	22.0000i	0.206559	+	1.13608i
$376$	−28.0000			−1.44399
$377$	−14.0000	−	14.0000i	−0.721037	−	0.721037i
$378$			24.0000i			1.23443i
$379$	−15.0000	−	15.0000i	−0.770498	−	0.770498i	0.207695	−	0.978194i	$-0.433404\pi$
$379$	−15.0000	−	15.0000i	−0.770498	−	0.770498i	−0.978194	+	0.207695i	$0.933404\pi$
$380$	18.0000	−	6.00000i	0.923381	−	0.307794i
$381$	14.0000	−	14.0000i	0.717242	−	0.717242i
$382$	18.0000	−	18.0000i	0.920960	−	0.920960i
$383$	5.00000	−	5.00000i	0.255488	−	0.255488i	−0.567728	−	0.823216i	$-0.692177\pi$
$383$	5.00000	−	5.00000i	0.255488	−	0.255488i	0.823216	+	0.567728i	$0.192177\pi$
$384$	−16.0000	−	16.0000i	−0.816497	−	0.816497i
$385$	−12.0000	−	6.00000i	−0.611577	−	0.305788i
$386$		−	30.0000i		−	1.52696i
$387$	−4.00000			−0.203331
$388$	−22.0000	−	22.0000i	−1.11688	−	1.11688i
$389$	23.0000	−	23.0000i	1.16615	−	1.16615i	0.183041	−	0.983105i	$-0.441406\pi$
$389$	23.0000	−	23.0000i	1.16615	−	1.16615i	0.983105	−	0.183041i	$-0.0585941\pi$
$390$	4.00000	+	12.0000i	0.202548	+	0.607644i
$391$	−2.00000			−0.101144
$392$	22.0000	+	22.0000i	1.11117	+	1.11117i
$393$	−14.0000	+	14.0000i	−0.706207	+	0.706207i
$394$	6.00000	+	6.00000i	0.302276	+	0.302276i
$395$	−8.00000	+	16.0000i	−0.402524	+	0.805047i
$396$	2.00000	+	2.00000i	0.100504	+	0.100504i
$397$			32.0000i			1.60603i	0.595956	+	0.803017i	$0.296773\pi$
$397$			32.0000i			1.60603i	−0.595956	+	0.803017i	$0.703227\pi$
$398$	10.0000	−	10.0000i	0.501255	−	0.501255i
$399$	36.0000			1.80225
$400$	12.0000	+	16.0000i	0.600000	+	0.800000i
$401$	−2.00000			−0.0998752			−0.0499376	−	0.998752i	$-0.515902\pi$
$401$	−2.00000			−0.0998752			−0.0499376	+	0.998752i	$0.515902\pi$
$402$	8.00000	−	8.00000i	0.399004	−	0.399004i
$403$			4.00000i			0.199254i
$404$	10.0000	−	10.0000i	0.497519	−	0.497519i
$405$	−11.0000	+	22.0000i	−0.546594	+	1.09319i
$406$	−42.0000	−	42.0000i	−2.08443	−	2.08443i
$407$	6.00000	−	6.00000i	0.297409	−	0.297409i
$408$	8.00000			0.396059
$409$	38.0000			1.87898			0.939490	−	0.342578i	$-0.111300\pi$
$409$	38.0000			1.87898			0.939490	+	0.342578i	$0.111300\pi$
$410$	4.00000	+	12.0000i	0.197546	+	0.592638i
$411$	18.0000	−	18.0000i	0.887875	−	0.887875i
$412$	10.0000	−	10.0000i	0.492665	−	0.492665i
$413$	18.0000			0.885722
$414$			2.00000i			0.0982946i
$415$	−4.00000	−	2.00000i	−0.196352	−	0.0981761i
$416$	8.00000	+	8.00000i	0.392232	+	0.392232i
$417$	18.0000	−	18.0000i	0.881464	−	0.881464i
$418$	−6.00000	+	6.00000i	−0.293470	+	0.293470i
$419$	−17.0000	+	17.0000i	−0.830504	+	0.830504i	−0.987586	−	0.157081i	$-0.949792\pi$
$419$	−17.0000	+	17.0000i	−0.830504	+	0.830504i	0.157081	+	0.987586i	$0.449792\pi$
$420$	12.0000	+	36.0000i	0.585540	+	1.75662i
$421$	−5.00000	−	5.00000i	−0.243685	−	0.243685i	0.574688	−	0.818373i	$-0.305124\pi$
$421$	−5.00000	−	5.00000i	−0.243685	−	0.243685i	−0.818373	+	0.574688i	$0.805124\pi$
$422$		−	38.0000i		−	1.84981i
$423$	−7.00000	−	7.00000i	−0.340352	−	0.340352i
$424$	16.0000	+	16.0000i	0.777029	+	0.777029i
$425$	−7.00000	−	1.00000i	−0.339550	−	0.0485071i
$426$		0			0
$427$		−	6.00000i		−	0.290360i
$428$	−12.0000			−0.580042
$429$	−4.00000	−	4.00000i	−0.193122	−	0.193122i
$430$	12.0000	−	4.00000i	0.578691	−	0.192897i
$431$		−	2.00000i		−	0.0963366i	−0.998839	−	0.0481683i	$-0.984662\pi$
$431$		−	2.00000i		−	0.0963366i	0.998839	−	0.0481683i	$-0.0153384\pi$
$432$			16.0000i			0.769800i
$433$	5.00000	+	5.00000i	0.240285	+	0.240285i	0.816968	−	0.576683i	$-0.195653\pi$
$433$	5.00000	+	5.00000i	0.240285	+	0.240285i	−0.576683	+	0.816968i	$0.695653\pi$
$434$			12.0000i			0.576018i
$435$	−14.0000	−	42.0000i	−0.671249	−	2.01375i
$436$	10.0000	−	10.0000i	0.478913	−	0.478913i
$437$	−6.00000			−0.287019
$438$			12.0000i			0.573382i
$439$		−	26.0000i		−	1.24091i	−0.784241	−	0.620456i	$-0.786947\pi$
$439$		−	26.0000i		−	1.24091i	0.784241	−	0.620456i	$-0.213053\pi$
$440$	−8.00000	−	4.00000i	−0.381385	−	0.190693i
$441$			11.0000i			0.523810i
$442$	−4.00000			−0.190261
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$	−24.0000			−1.13899
$445$	6.00000	−	12.0000i	0.284427	−	0.568855i
$446$	18.0000			0.852325
$447$	2.00000	+	2.00000i	0.0945968	+	0.0945968i
$448$	24.0000	+	24.0000i	1.13389	+	1.13389i
$449$		−	24.0000i		−	1.13263i	−0.824189	−	0.566315i	$-0.808369\pi$
$449$		−	24.0000i		−	1.13263i	0.824189	−	0.566315i	$-0.191631\pi$
$450$	−1.00000	+	7.00000i	−0.0471405	+	0.329983i
$451$	−4.00000	−	4.00000i	−0.188353	−	0.188353i
$452$	−26.0000	+	26.0000i	−1.22294	+	1.22294i
$453$		−	16.0000i		−	0.751746i
$454$	12.0000	+	12.0000i	0.563188	+	0.563188i
$455$	−6.00000	−	18.0000i	−0.281284	−	0.843853i
$456$	24.0000			1.12390
$457$	−7.00000	−	7.00000i	−0.327446	−	0.327446i	0.524168	−	0.851615i	$-0.324376\pi$
$457$	−7.00000	−	7.00000i	−0.327446	−	0.327446i	−0.851615	+	0.524168i	$0.824376\pi$
$458$	−2.00000			−0.0934539
$459$	−4.00000	−	4.00000i	−0.186704	−	0.186704i
$460$	−2.00000	−	6.00000i	−0.0932505	−	0.279751i
$461$	−21.0000	+	21.0000i	−0.978068	+	0.978068i	−0.999765	−	0.0216971i	$-0.993093\pi$
$461$	−21.0000	+	21.0000i	−0.978068	+	0.978068i	0.0216971	+	0.999765i	$0.493093\pi$
$462$	−12.0000	−	12.0000i	−0.558291	−	0.558291i
$463$	−19.0000	+	19.0000i	−0.883005	+	0.883005i	−0.993839	−	0.110834i	$-0.964648\pi$
$463$	−19.0000	+	19.0000i	−0.883005	+	0.883005i	0.110834	+	0.993839i	$0.464648\pi$
$464$	−28.0000	−	28.0000i	−1.29987	−	1.29987i
$465$	−4.00000	+	8.00000i	−0.185496	+	0.370991i
$466$	18.0000			0.833834
$467$	−28.0000			−1.29569			−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000			−1.29569			−0.647843	+	0.761774i	$0.724329\pi$
$468$			4.00000i			0.184900i
$469$	−12.0000	+	12.0000i	−0.554109	+	0.554109i
$470$	28.0000	+	14.0000i	1.29154	+	0.645772i
$471$	−40.0000			−1.84310
$472$	12.0000			0.552345
$473$	−4.00000	+	4.00000i	−0.183920	+	0.183920i
$474$	−16.0000	+	16.0000i	−0.734904	+	0.734904i
$475$	−21.0000	−	3.00000i	−0.963546	−	0.137649i
$476$	−12.0000			−0.550019
$477$			8.00000i			0.366295i
$478$		0			0
$479$	32.0000			1.46212			0.731059	−	0.682315i	$-0.239027\pi$
$479$	32.0000			1.46212			0.731059	+	0.682315i	$0.239027\pi$
$480$	8.00000	+	24.0000i	0.365148	+	1.09545i
$481$	12.0000			0.547153
$482$	−14.0000	−	14.0000i	−0.637683	−	0.637683i
$483$		−	12.0000i		−	0.546019i
$484$	−18.0000			−0.818182
$485$	11.0000	+	33.0000i	0.499484	+	1.49845i
$486$	−10.0000	+	10.0000i	−0.453609	+	0.453609i
$487$	−15.0000	+	15.0000i	−0.679715	+	0.679715i	−0.959936	−	0.280221i	$-0.909592\pi$
$487$	−15.0000	+	15.0000i	−0.679715	+	0.679715i	0.280221	+	0.959936i	$0.409592\pi$
$488$		−	4.00000i		−	0.181071i
$489$	28.0000			1.26620
$490$	−11.0000	−	33.0000i	−0.496929	−	1.49079i
$491$	−9.00000	+	9.00000i	−0.406164	+	0.406164i	−0.880399	−	0.474234i	$-0.842725\pi$
$491$	−9.00000	+	9.00000i	−0.406164	+	0.406164i	0.474234	+	0.880399i	$0.342725\pi$
$492$			16.0000i			0.721336i
$493$	14.0000			0.630528
$494$	−12.0000			−0.539906
$495$	−1.00000	−	3.00000i	−0.0449467	−	0.134840i
$496$			8.00000i			0.359211i
$497$		0			0
$498$	−4.00000	−	4.00000i	−0.179244	−	0.179244i
$499$	−29.0000	+	29.0000i	−1.29822	+	1.29822i	−0.368650	+	0.929568i	$0.620180\pi$
$499$	−29.0000	+	29.0000i	−1.29822	+	1.29822i	−0.929568	+	0.368650i	$0.879820\pi$
$500$	−4.00000	−	22.0000i	−0.178885	−	0.983870i
$501$	6.00000	+	6.00000i	0.268060	+	0.268060i
$502$	22.0000			0.981908
$503$	−29.0000	−	29.0000i	−1.29305	−	1.29305i	−0.932893	−	0.360153i	$-0.882725\pi$
$503$	−29.0000	−	29.0000i	−1.29305	−	1.29305i	−0.360153	−	0.932893i	$-0.617275\pi$
$504$			12.0000i			0.534522i
$505$	−15.0000	+	5.00000i	−0.667491	+	0.222497i
$506$	2.00000	+	2.00000i	0.0889108	+	0.0889108i
$507$			18.0000i			0.799408i
$508$	−14.0000	+	14.0000i	−0.621150	+	0.621150i
$509$	−17.0000	−	17.0000i	−0.753512	−	0.753512i	0.221621	−	0.975133i	$-0.428865\pi$
$509$	−17.0000	−	17.0000i	−0.753512	−	0.753512i	−0.975133	+	0.221621i	$0.928865\pi$
$510$	−8.00000	−	4.00000i	−0.354246	−	0.177123i
$511$		−	18.0000i		−	0.796273i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	−12.0000	−	12.0000i	−0.529813	−	0.529813i
$514$	26.0000			1.14681
$515$	−15.0000	+	5.00000i	−0.660979	+	0.220326i
$516$	16.0000			0.704361
$517$	−14.0000			−0.615719
$518$	36.0000			1.58175
$519$			12.0000i			0.526742i
$520$	−4.00000	−	12.0000i	−0.175412	−	0.526235i
$521$			16.0000i			0.700973i	0.936568	+	0.350486i	$0.113984\pi$
$521$			16.0000i			0.700973i	−0.936568	+	0.350486i	$0.886016\pi$
$522$		−	14.0000i		−	0.612763i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	14.0000	−	14.0000i	0.611593	−	0.611593i
$525$	6.00000	−	42.0000i	0.261861	−	1.83303i
$526$			14.0000i			0.610429i
$527$	−2.00000	−	2.00000i	−0.0871214	−	0.0871214i
$528$	−8.00000	−	8.00000i	−0.348155	−	0.348155i
$529$		−	21.0000i		−	0.913043i
$530$	−8.00000	−	24.0000i	−0.347498	−	1.04249i
$531$	3.00000	+	3.00000i	0.130189	+	0.130189i
$532$	−36.0000			−1.56080
$533$		−	8.00000i		−	0.346518i
$534$	12.0000	−	12.0000i	0.519291	−	0.519291i
$535$	12.0000	+	6.00000i	0.518805	+	0.259403i
$536$	−8.00000	+	8.00000i	−0.345547	+	0.345547i
$537$	10.0000	+	10.0000i	0.431532	+	0.431532i
$538$		−	2.00000i		−	0.0862261i
$539$	11.0000	+	11.0000i	0.473804	+	0.473804i
$540$	8.00000	−	16.0000i	0.344265	−	0.688530i
$541$	15.0000	−	15.0000i	0.644900	−	0.644900i	−0.306856	−	0.951756i	$-0.599277\pi$
$541$	15.0000	−	15.0000i	0.644900	−	0.644900i	0.951756	+	0.306856i	$0.0992769\pi$
$542$	−30.0000	+	30.0000i	−1.28861	+	1.28861i
$543$	6.00000	−	6.00000i	0.257485	−	0.257485i
$544$	−8.00000			−0.342997
$545$	−15.0000	+	5.00000i	−0.642529	+	0.214176i
$546$		−	24.0000i		−	1.02711i
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	−18.0000	+	18.0000i	−0.768922	+	0.768922i
$549$	1.00000	−	1.00000i	0.0426790	−	0.0426790i
$550$	6.00000	+	8.00000i	0.255841	+	0.341121i
$551$	42.0000			1.78926
$552$		−	8.00000i		−	0.340503i
$553$	24.0000	−	24.0000i	1.02058	−	1.02058i
$554$	18.0000	+	18.0000i	0.764747	+	0.764747i
$555$	24.0000	+	12.0000i	1.01874	+	0.509372i
$556$	−18.0000	+	18.0000i	−0.763370	+	0.763370i
$557$		−	28.0000i		−	1.18640i	−0.805056	−	0.593199i	$-0.797865\pi$
$557$		−	28.0000i		−	1.18640i	0.805056	−	0.593199i	$-0.202135\pi$
$558$	−2.00000	+	2.00000i	−0.0846668	+	0.0846668i
$559$	−8.00000			−0.338364
$560$	−12.0000	−	36.0000i	−0.507093	−	1.52128i
$561$	4.00000			0.168880
$562$	16.0000	−	16.0000i	0.674919	−	0.674919i
$563$		−	18.0000i		−	0.758610i	−0.925272	−	0.379305i	$-0.876163\pi$
$563$		−	18.0000i		−	0.758610i	0.925272	−	0.379305i	$-0.123837\pi$
$564$	28.0000	+	28.0000i	1.17901	+	1.17901i
$565$	39.0000	−	13.0000i	1.64074	−	0.546914i
$566$	12.0000	+	12.0000i	0.504398	+	0.504398i
$567$	33.0000	−	33.0000i	1.38587	−	1.38587i
$568$		0			0
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$	−24.0000	−	12.0000i	−1.00525	−	0.502625i
$571$	−25.0000	+	25.0000i	−1.04622	+	1.04622i	−0.0473385	+	0.998879i	$0.515074\pi$
$571$	−25.0000	+	25.0000i	−1.04622	+	1.04622i	−0.998879	+	0.0473385i	$0.984926\pi$
$572$	4.00000	+	4.00000i	0.167248	+	0.167248i
$573$	−36.0000			−1.50392
$574$		−	24.0000i		−	1.00174i
$575$	−1.00000	+	7.00000i	−0.0417029	+	0.291920i
$576$			8.00000i			0.333333i
$577$	9.00000	−	9.00000i	0.374675	−	0.374675i	−0.494502	−	0.869177i	$-0.664649\pi$
$577$	9.00000	−	9.00000i	0.374675	−	0.374675i	0.869177	+	0.494502i	$0.164649\pi$
$578$	−15.0000	+	15.0000i	−0.623918	+	0.623918i
$579$	−30.0000	+	30.0000i	−1.24676	+	1.24676i
$580$	14.0000	+	42.0000i	0.581318	+	1.74396i
$581$	6.00000	+	6.00000i	0.248922	+	0.248922i
$582$			44.0000i			1.82386i
$583$	8.00000	+	8.00000i	0.331326	+	0.331326i
$584$		−	12.0000i		−	0.496564i
$585$	2.00000	−	4.00000i	0.0826898	−	0.165380i
$586$	12.0000	−	12.0000i	0.495715	−	0.495715i
$587$		−	2.00000i		−	0.0825488i	−0.999148	−	0.0412744i	$-0.986858\pi$
$587$		−	2.00000i		−	0.0825488i	0.999148	−	0.0412744i	$-0.0131418\pi$
$588$		−	44.0000i		−	1.81453i
$589$	−6.00000	−	6.00000i	−0.247226	−	0.247226i
$590$	−12.0000	−	6.00000i	−0.494032	−	0.247016i
$591$		−	12.0000i		−	0.493614i
$592$	24.0000			0.986394
$593$	17.0000	+	17.0000i	0.698106	+	0.698106i	0.964002	−	0.265896i	$-0.0856676\pi$
$593$	17.0000	+	17.0000i	0.698106	+	0.698106i	−0.265896	+	0.964002i	$0.585668\pi$
$594$			8.00000i			0.328244i
$595$	12.0000	+	6.00000i	0.491952	+	0.245976i
$596$	−2.00000	−	2.00000i	−0.0819232	−	0.0819232i
$597$	−20.0000			−0.818546
$598$			4.00000i			0.163572i
$599$			30.0000i			1.22577i	0.790173	+	0.612883i	$0.209990\pi$
$599$			30.0000i			1.22577i	−0.790173	+	0.612883i	$0.790010\pi$
$600$	4.00000	−	28.0000i	0.163299	−	1.14310i
$601$		−	16.0000i		−	0.652654i	−0.945257	−	0.326327i	$-0.894189\pi$
$601$		−	16.0000i		−	0.652654i	0.945257	−	0.326327i	$-0.105811\pi$
$602$	−24.0000			−0.978167
$603$	−4.00000			−0.162893
$604$			16.0000i			0.651031i
$605$	18.0000	+	9.00000i	0.731804	+	0.365902i
$606$	−20.0000			−0.812444
$607$	23.0000	+	23.0000i	0.933541	+	0.933541i	0.997925	−	0.0643840i	$-0.0205082\pi$
$607$	23.0000	+	23.0000i	0.933541	+	0.933541i	−0.0643840	+	0.997925i	$0.520508\pi$
$608$	−24.0000			−0.973329
$609$			84.0000i			3.40385i
$610$	−2.00000	+	4.00000i	−0.0809776	+	0.161955i
$611$	−14.0000	−	14.0000i	−0.566379	−	0.566379i
$612$	−2.00000	−	2.00000i	−0.0808452	−	0.0808452i
$613$			8.00000i			0.323117i	0.986863	+	0.161558i	$0.0516520\pi$
$613$			8.00000i			0.323117i	−0.986863	+	0.161558i	$0.948348\pi$
$614$	−4.00000	−	4.00000i	−0.161427	−	0.161427i
$615$	8.00000	−	16.0000i	0.322591	−	0.645182i
$616$	12.0000	+	12.0000i	0.483494	+	0.483494i
$617$	25.0000	+	25.0000i	1.00646	+	1.00646i	0.999979	+	0.00648312i	$0.00206366\pi$
$617$	25.0000	+	25.0000i	1.00646	+	1.00646i	0.00648312	+	0.999979i	$0.497936\pi$
$618$	−20.0000			−0.804518
$619$	−7.00000	−	7.00000i	−0.281354	−	0.281354i	0.552295	−	0.833649i	$-0.313752\pi$
$619$	−7.00000	−	7.00000i	−0.281354	−	0.281354i	−0.833649	+	0.552295i	$0.813752\pi$
$620$	4.00000	−	8.00000i	0.160644	−	0.321288i
$621$	−4.00000	+	4.00000i	−0.160514	+	0.160514i
$622$	16.0000	+	16.0000i	0.641542	+	0.641542i
$623$	−18.0000	+	18.0000i	−0.721155	+	0.721155i
$624$		−	16.0000i		−	0.640513i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	26.0000			1.03917
$627$	12.0000			0.479234
$628$	40.0000			1.59617
$629$	−6.00000	+	6.00000i	−0.239236	+	0.239236i
$630$	6.00000	−	12.0000i	0.239046	−	0.478091i
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$	16.0000	−	16.0000i	0.636446	−	0.636446i
$633$	−38.0000	+	38.0000i	−1.51036	+	1.51036i
$634$	8.00000	−	8.00000i	0.317721	−	0.317721i
$635$	21.0000	−	7.00000i	0.833360	−	0.277787i
$636$		−	32.0000i		−	1.26888i
$637$			22.0000i			0.871672i
$638$	−14.0000	−	14.0000i	−0.554265	−	0.554265i
$639$		0			0
$640$	−8.00000	−	24.0000i	−0.316228	−	0.948683i
$641$	−30.0000			−1.18493			−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000			−1.18493			−0.592464	+	0.805597i	$0.701845\pi$
$642$	12.0000	+	12.0000i	0.473602	+	0.473602i
$643$		−	26.0000i		−	1.02534i	−0.858586	−	0.512670i	$-0.828656\pi$
$643$		−	26.0000i		−	1.02534i	0.858586	−	0.512670i	$-0.171344\pi$
$644$			12.0000i			0.472866i
$645$	−16.0000	−	8.00000i	−0.629999	−	0.315000i
$646$	6.00000	−	6.00000i	0.236067	−	0.236067i
$647$	−15.0000	+	15.0000i	−0.589711	+	0.589711i	−0.937553	−	0.347842i	$-0.886914\pi$
$647$	−15.0000	+	15.0000i	−0.589711	+	0.589711i	0.347842	+	0.937553i	$0.386914\pi$
$648$	22.0000	−	22.0000i	0.864242	−	0.864242i
$649$	6.00000			0.235521
$650$	−2.00000	+	14.0000i	−0.0784465	+	0.549125i
$651$	12.0000	−	12.0000i	0.470317	−	0.470317i
$652$	−28.0000			−1.09656
$653$	−2.00000			−0.0782660			−0.0391330	−	0.999234i	$-0.512460\pi$
$653$	−2.00000			−0.0782660			−0.0391330	+	0.999234i	$0.512460\pi$
$654$	−20.0000			−0.782062
$655$	−21.0000	+	7.00000i	−0.820538	+	0.273513i
$656$		−	16.0000i		−	0.624695i
$657$	3.00000	−	3.00000i	0.117041	−	0.117041i
$658$	−42.0000	−	42.0000i	−1.63733	−	1.63733i
$659$	11.0000	−	11.0000i	0.428499	−	0.428499i	−0.459618	−	0.888117i	$-0.652014\pi$
$659$	11.0000	−	11.0000i	0.428499	−	0.428499i	0.888117	+	0.459618i	$0.152014\pi$
$660$	4.00000	+	12.0000i	0.155700	+	0.467099i
$661$	−25.0000	−	25.0000i	−0.972387	−	0.972387i	0.0272416	−	0.999629i	$-0.491328\pi$
$661$	−25.0000	−	25.0000i	−0.972387	−	0.972387i	−0.999629	+	0.0272416i	$0.991328\pi$
$662$	−42.0000			−1.63238
$663$	4.00000	+	4.00000i	0.155347	+	0.155347i
$664$	4.00000	+	4.00000i	0.155230	+	0.155230i
$665$	36.0000	+	18.0000i	1.39602	+	0.698010i
$666$	6.00000	+	6.00000i	0.232495	+	0.232495i
$667$		−	14.0000i		−	0.542082i
$668$	−6.00000	−	6.00000i	−0.232147	−	0.232147i
$669$	−18.0000	−	18.0000i	−0.695920	−	0.695920i
$670$	12.0000	−	4.00000i	0.463600	−	0.154533i
$671$		−	2.00000i		−	0.0772091i
$672$		−	48.0000i		−	1.85164i
$673$	1.00000	+	1.00000i	0.0385472	+	0.0385472i	0.726118	−	0.687570i	$-0.241323\pi$
$673$	1.00000	+	1.00000i	0.0385472	+	0.0385472i	−0.687570	+	0.726118i	$0.741323\pi$
$674$	−22.0000			−0.847408
$675$	−16.0000	+	12.0000i	−0.615840	+	0.461880i
$676$		−	18.0000i		−	0.692308i
$677$	−42.0000			−1.61419			−0.807096	−	0.590421i	$-0.798962\pi$
$677$	−42.0000			−1.61419			−0.807096	+	0.590421i	$0.798962\pi$
$678$	52.0000			1.99705
$679$		−	66.0000i		−	2.53285i
$680$	8.00000	+	4.00000i	0.306786	+	0.153393i
$681$		−	24.0000i		−	0.919682i
$682$			4.00000i			0.153168i
$683$	−4.00000			−0.153056			−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000			−0.153056			−0.0765279	+	0.997067i	$0.524383\pi$
$684$	−6.00000	−	6.00000i	−0.229416	−	0.229416i
$685$	27.0000	−	9.00000i	1.03162	−	0.343872i
$686$			24.0000i			0.916324i
$687$	2.00000	+	2.00000i	0.0763048	+	0.0763048i
$688$	−16.0000			−0.609994
$689$			16.0000i			0.609551i
$690$	−4.00000	+	8.00000i	−0.152277	+	0.304555i
$691$	21.0000	+	21.0000i	0.798878	+	0.798878i	0.982919	−	0.184041i	$-0.0589179\pi$
$691$	21.0000	+	21.0000i	0.798878	+	0.798878i	−0.184041	+	0.982919i	$0.558918\pi$
$692$		−	12.0000i		−	0.456172i
$693$			6.00000i			0.227921i
$694$	2.00000	−	2.00000i	0.0759190	−	0.0759190i
$695$	27.0000	−	9.00000i	1.02417	−	0.341389i
$696$			56.0000i			2.12267i
$697$	4.00000	+	4.00000i	0.151511	+	0.151511i
$698$			6.00000i			0.227103i
$699$	−18.0000	−	18.0000i	−0.680823	−	0.680823i
$700$	−6.00000	+	42.0000i	−0.226779	+	1.58745i
$701$	−13.0000	+	13.0000i	−0.491003	+	0.491003i	−0.908622	−	0.417619i	$-0.862865\pi$
$701$	−13.0000	+	13.0000i	−0.491003	+	0.491003i	0.417619	+	0.908622i	$0.362865\pi$
$702$	−8.00000	+	8.00000i	−0.301941	+	0.301941i
$703$	−18.0000	+	18.0000i	−0.678883	+	0.678883i
$704$	8.00000	+	8.00000i	0.301511	+	0.301511i
$705$	−14.0000	−	42.0000i	−0.527271	−	1.58181i
$706$			26.0000i			0.978523i
$707$	30.0000			1.12827
$708$	−12.0000	−	12.0000i	−0.450988	−	0.450988i
$709$	−1.00000	+	1.00000i	−0.0375558	+	0.0375558i	−0.725635	−	0.688080i	$-0.758454\pi$
$709$	−1.00000	+	1.00000i	−0.0375558	+	0.0375558i	0.688080	+	0.725635i	$0.258454\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$	−12.0000	+	12.0000i	−0.449719	+	0.449719i
$713$	−2.00000	+	2.00000i	−0.0749006	+	0.0749006i
$714$	12.0000	+	12.0000i	0.449089	+	0.449089i
$715$	−2.00000	−	6.00000i	−0.0747958	−	0.224387i
$716$	−10.0000	−	10.0000i	−0.373718	−	0.373718i
$717$		0			0
$718$	−14.0000	+	14.0000i	−0.522475	+	0.522475i
$719$	32.0000			1.19340			0.596699	−	0.802465i	$-0.296479\pi$
$719$	32.0000			1.19340			0.596699	+	0.802465i	$0.296479\pi$
$720$	4.00000	−	8.00000i	0.149071	−	0.298142i
$721$	30.0000			1.11726
$722$	−1.00000	+	1.00000i	−0.0372161	+	0.0372161i
$723$			28.0000i			1.04133i
$724$	−6.00000	+	6.00000i	−0.222988	+	0.222988i
$725$	7.00000	−	49.0000i	0.259973	−	1.81981i
$726$	18.0000	+	18.0000i	0.668043	+	0.668043i
$727$	−7.00000	+	7.00000i	−0.259616	+	0.259616i	−0.824898	−	0.565282i	$-0.808767\pi$
$727$	−7.00000	+	7.00000i	−0.259616	+	0.259616i	0.565282	+	0.824898i	$0.308767\pi$
$728$			24.0000i			0.889499i
$729$	−13.0000			−0.481481
$730$	−6.00000	+	12.0000i	−0.222070	+	0.444140i
$731$	4.00000	−	4.00000i	0.147945	−	0.147945i
$732$	−4.00000	+	4.00000i	−0.147844	+	0.147844i
$733$	−30.0000			−1.10808			−0.554038	−	0.832492i	$-0.686914\pi$
$733$	−30.0000			−1.10808			−0.554038	+	0.832492i	$0.686914\pi$
$734$		−	42.0000i		−	1.55025i
$735$	−22.0000	+	44.0000i	−0.811482	+	1.62296i
$736$			8.00000i			0.294884i
$737$	−4.00000	+	4.00000i	−0.147342	+	0.147342i
$738$	4.00000	−	4.00000i	0.147242	−	0.147242i
$739$	−21.0000	+	21.0000i	−0.772497	+	0.772497i	−0.978543	−	0.206045i	$-0.933941\pi$
$739$	−21.0000	+	21.0000i	−0.772497	+	0.772497i	0.206045	+	0.978543i	$0.433941\pi$
$740$	−24.0000	−	12.0000i	−0.882258	−	0.441129i
$741$	12.0000	+	12.0000i	0.440831	+	0.440831i
$742$			48.0000i			1.76214i
$743$	31.0000	+	31.0000i	1.13728	+	1.13728i	0.988936	+	0.148344i	$0.0473942\pi$
$743$	31.0000	+	31.0000i	1.13728	+	1.13728i	0.148344	+	0.988936i	$0.452606\pi$
$744$	8.00000	−	8.00000i	0.293294	−	0.293294i
$745$	1.00000	+	3.00000i	0.0366372	+	0.109911i
$746$	4.00000	−	4.00000i	0.146450	−	0.146450i
$747$			2.00000i			0.0731762i
$748$	−4.00000			−0.146254
$749$	−18.0000	−	18.0000i	−0.657706	−	0.657706i
$750$	−18.0000	+	26.0000i	−0.657267	+	0.949386i
$751$		−	50.0000i		−	1.82453i	−0.409605	−	0.912263i	$-0.634333\pi$
$751$		−	50.0000i		−	1.82453i	0.409605	−	0.912263i	$-0.365667\pi$
$752$	−28.0000	−	28.0000i	−1.02105	−	1.02105i
$753$	−22.0000	−	22.0000i	−0.801725	−	0.801725i
$754$		−	28.0000i		−	1.01970i
$755$	8.00000	−	16.0000i	0.291150	−	0.582300i
$756$	−24.0000	+	24.0000i	−0.872872	+	0.872872i
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$		−	30.0000i		−	1.08965i
$759$		−	4.00000i		−	0.145191i
$760$	24.0000	+	12.0000i	0.870572	+	0.435286i
$761$		−	40.0000i		−	1.45000i	−0.688749	−	0.724999i	$-0.741840\pi$
$761$		−	40.0000i		−	1.45000i	0.688749	−	0.724999i	$-0.258160\pi$
$762$	28.0000			1.01433
$763$	30.0000			1.08607
$764$	36.0000			1.30243
$765$	1.00000	+	3.00000i	0.0361551	+	0.108465i
$766$	10.0000			0.361315
$767$	6.00000	+	6.00000i	0.216647	+	0.216647i
$768$		−	32.0000i		−	1.15470i
$769$		−	4.00000i		−	0.144244i	−0.997396	−	0.0721218i	$-0.977023\pi$
$769$		−	4.00000i		−	0.144244i	0.997396	−	0.0721218i	$-0.0229770\pi$
$770$	−6.00000	−	18.0000i	−0.216225	−	0.648675i
$771$	−26.0000	−	26.0000i	−0.936367	−	0.936367i
$772$	30.0000	−	30.0000i	1.07972	−	1.07972i
$773$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} -2.00000i q^{3} +2.00000i q^{4} +(1.00000 - 2.00000i) q^{5} +(2.00000 - 2.00000i) q^{6} +(-3.00000 + 3.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} -1.00000 q^{9} +(3.00000 - 1.00000i) q^{10} +(-1.00000 + 1.00000i) q^{11} +4.00000 q^{12} -2.00000 q^{13} -6.00000 q^{14} +(-4.00000 - 2.00000i) q^{15} -4.00000 q^{16} +(1.00000 - 1.00000i) q^{17} +(-1.00000 - 1.00000i) q^{18} +(3.00000 - 3.00000i) q^{19} +(4.00000 + 2.00000i) q^{20} +(6.00000 + 6.00000i) q^{21} -2.00000 q^{22} +(-1.00000 - 1.00000i) q^{23} +(4.00000 + 4.00000i) q^{24} +(-3.00000 - 4.00000i) q^{25} +(-2.00000 - 2.00000i) q^{26} -4.00000i q^{27} +(-6.00000 - 6.00000i) q^{28} +(7.00000 + 7.00000i) q^{29} +(-2.00000 - 6.00000i) q^{30} -2.00000i q^{31} +(-4.00000 - 4.00000i) q^{32} +(2.00000 + 2.00000i) q^{33} +2.00000 q^{34} +(3.00000 + 9.00000i) q^{35} -2.00000i q^{36} -6.00000 q^{37} +6.00000 q^{38} +4.00000i q^{39} +(2.00000 + 6.00000i) q^{40} +4.00000i q^{41} +12.0000i q^{42} +4.00000 q^{43} +(-2.00000 - 2.00000i) q^{44} +(-1.00000 + 2.00000i) q^{45} -2.00000i q^{46} +(7.00000 + 7.00000i) q^{47} +8.00000i q^{48} -11.0000i q^{49} +(1.00000 - 7.00000i) q^{50} +(-2.00000 - 2.00000i) q^{51} -4.00000i q^{52} -8.00000i q^{53} +(4.00000 - 4.00000i) q^{54} +(1.00000 + 3.00000i) q^{55} -12.0000i q^{56} +(-6.00000 - 6.00000i) q^{57} +14.0000i q^{58} +(-3.00000 - 3.00000i) q^{59} +(4.00000 - 8.00000i) q^{60} +(-1.00000 + 1.00000i) q^{61} +(2.00000 - 2.00000i) q^{62} +(3.00000 - 3.00000i) q^{63} -8.00000i q^{64} +(-2.00000 + 4.00000i) q^{65} +4.00000i q^{66} +4.00000 q^{67} +(2.00000 + 2.00000i) q^{68} +(-2.00000 + 2.00000i) q^{69} +(-6.00000 + 12.0000i) q^{70} +(2.00000 - 2.00000i) q^{72} +(-3.00000 + 3.00000i) q^{73} +(-6.00000 - 6.00000i) q^{74} +(-8.00000 + 6.00000i) q^{75} +(6.00000 + 6.00000i) q^{76} -6.00000i q^{77} +(-4.00000 + 4.00000i) q^{78} -8.00000 q^{79} +(-4.00000 + 8.00000i) q^{80} -11.0000 q^{81} +(-4.00000 + 4.00000i) q^{82} -2.00000i q^{83} +(-12.0000 + 12.0000i) q^{84} +(-1.00000 - 3.00000i) q^{85} +(4.00000 + 4.00000i) q^{86} +(14.0000 - 14.0000i) q^{87} -4.00000i q^{88} +6.00000 q^{89} +(-3.00000 + 1.00000i) q^{90} +(6.00000 - 6.00000i) q^{91} +(2.00000 - 2.00000i) q^{92} -4.00000 q^{93} +14.0000i q^{94} +(-3.00000 - 9.00000i) q^{95} +(-8.00000 + 8.00000i) q^{96} +(-11.0000 + 11.0000i) q^{97} +(11.0000 - 11.0000i) q^{98} +(1.00000 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{5} + 4 q^{6} - 6 q^{7} - 4 q^{8} - 2 q^{9} + 6 q^{10} - 2 q^{11} + 8 q^{12} - 4 q^{13} - 12 q^{14} - 8 q^{15} - 8 q^{16} + 2 q^{17} - 2 q^{18} + 6 q^{19} + 8 q^{20} + 12 q^{21} - 4 q^{22}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^5 + 4 * q^6 - 6 * q^7 - 4 * q^8 - 2 * q^9 + 6 * q^10 - 2 * q^11 + 8 * q^12 - 4 * q^13 - 12 * q^14 - 8 * q^15 - 8 * q^16 + 2 * q^17 - 2 * q^18 + 6 * q^19 + 8 * q^20 + 12 * q^21 - 4 * q^22 - 2 * q^23 + 8 * q^24 - 6 * q^25 - 4 * q^26 - 12 * q^28 + 14 * q^29 - 4 * q^30 - 8 * q^32 + 4 * q^33 + 4 * q^34 + 6 * q^35 - 12 * q^37 + 12 * q^38 + 4 * q^40 + 8 * q^43 - 4 * q^44 - 2 * q^45 + 14 * q^47 + 2 * q^50 - 4 * q^51 + 8 * q^54 + 2 * q^55 - 12 * q^57 - 6 * q^59 + 8 * q^60 - 2 * q^61 + 4 * q^62 + 6 * q^63 - 4 * q^65 + 8 * q^67 + 4 * q^68 - 4 * q^69 - 12 * q^70 + 4 * q^72 - 6 * q^73 - 12 * q^74 - 16 * q^75 + 12 * q^76 - 8 * q^78 - 16 * q^79 - 8 * q^80 - 22 * q^81 - 8 * q^82 - 24 * q^84 - 2 * q^85 + 8 * q^86 + 28 * q^87 + 12 * q^89 - 6 * q^90 + 12 * q^91 + 4 * q^92 - 8 * q^93 - 6 * q^95 - 16 * q^96 - 22 * q^97 + 22 * q^98 + 2 * q^99

Introduction

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